Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 84)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.59182215273.1	x^12 - 5x^11 + 14x^10 - 31x^9 + 53x^8 - 72x^7 + 81x^6 - 72x^5 + 53x^4 - 31x^3 + 14x^2 - 5x + 1	\( 3^{6}\cdot 433^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.126759838761.1	x^12 - 3x^11 + 6x^10 - 11x^9 + 15x^8 - 18x^7 + 21x^6 - 18x^5 + 15x^4 - 11x^3 + 6x^2 - 3x + 1	\( 3^{13}\cdot 43^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.218711265625.1	x^12 - 3x^11 + 8x^10 - 17x^9 + 29x^8 - 40x^7 + 45x^6 - 40x^5 + 29x^4 - 17x^3 + 8x^2 - 3x + 1	\( 5^{6}\cdot 241^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.239251750912.1	x^12 - 2x^11 + 5x^10 - 8x^9 + 11x^8 - 14x^7 + 15x^6 - 14x^5 + 11x^4 - 8x^3 + 5x^2 - 2x + 1	\( 2^{18}\cdot 97^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.3495224609375.1	x^12 - x^11 - 4x^10 + 5x^9 - 5x^8 + 14x^7 - 19x^6 + 14x^5 - 5x^4 + 5x^3 - 4x^2 - x + 1	\( -\,5^{10}\cdot 71^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.5156831600217.1	x^12 - x^11 - 2x^10 + 4x^9 + 6x^8 - 27x^7 + 41x^6 - 27x^5 + 6x^4 + 4x^3 - 2x^2 - x + 1	\( 3^{7}\cdot 11^{9} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.6815156734375.1	x^12 - 2x^11 - 2x^10 + 11x^9 - 6x^8 - 21x^7 + 19x^6 + 12x^5 - 19x^4 + 2x^3 + 8x^2 - x - 1	\( -\,5^{6}\cdot 11^{4}\cdot 31^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.11209998860288.1	x^12 - 6x^10 - 4x^9 + 11x^8 + 8x^7 - 6x^6 + 8x^5 + 14x^4 + 8x^3 + 16x^2 + 16x + 8	\( 2^{27}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T35)	Trivial (GRH)
12.0.18786186952704.1	x^12 - 4x^11 + 10x^10 - 12x^9 + x^8 + 24x^7 - 32x^6 - 8x^5 + 90x^4 - 144x^3 + 128x^2 - 64x + 16	\( 2^{33}\cdot 3^{7} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.42845606719488.1	x^12 - 2x^9 + 6x^6 - 2x^3 + 1	\( 2^{12}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.104513734180864.1	x^12 + 4x^10 + 4x^8 - 12x^6 - 27x^4 + 48x^2 + 46	\( 2^{33}\cdot 23^{3} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.0.107567821094912.2	x^12 - 6x^11 + 21x^10 - 40x^9 + 67x^8 - 82x^7 + 95x^6 - 82x^5 + 67x^4 - 40x^3 + 21x^2 - 6x + 1	\( 2^{18}\cdot 17^{7} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.125765232361472.7	x^12 - 4x^10 + 2x^8 + 4x^6 + 9x^4 - 16x^2 + 8	\( 2^{33}\cdot 11^{4} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.190210142896128.1	x^12 - 4x^9 + 10x^8 - 4x^7 + 8x^6 - 12x^5 + 3x^4 - 36x^3 + 12x^2 + 24x + 6	\( 2^{30}\cdot 3^{11} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.213986410758144.1	x^12 + 6x^10 + 12x^8 + 24x^6 + 21x^4 - 6x^2 + 6	\( 2^{27}\cdot 3^{13} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.0.641959232274432.3	x^12 - 6x^10 + 12x^8 - 12x^6 + 45x^4 - 54x^2 + 18	\( 2^{27}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.6.717439927058432.1	x^12 - 4x^10 - 12x^8 + 28x^6 - 59x^4 + 32x^2 - 2	\( -\,2^{33}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.884272562962432.1	x^12 - 4x^11 + 8x^10 - 24x^9 + 60x^8 - 96x^7 + 176x^6 - 312x^5 + 325x^4 - 252x^3 + 328x^2 - 352x + 146	\( 2^{30}\cdot 7^{7} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.12.913378856890625.1	x^12 - x^11 - 18x^10 + 8x^9 + 95x^8 - 14x^7 - 165x^6 + 23x^5 + 110x^4 - 17x^3 - 24x^2 + 2x + 1	\( 5^{6}\cdot 3881^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.971471884263424.1	x^12 - 3x^11 + 11x^10 - 26x^9 + 65x^8 - 103x^7 + 126x^6 - 103x^5 + 65x^4 - 26x^3 + 11x^2 - 3x + 1	\( 2^{13}\cdot 17^{9} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.6.991623123042304.1	x^12 + 2x^10 - 29x^8 + 88x^6 - 128x^4 + 72x^2 - 4	\( -\,2^{30}\cdot 31^{4} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.1032188877029888.1	x^12 - 5x^11 + 16x^10 - 42x^9 + 80x^8 - 82x^7 + 14x^6 + 29x^5 + 39x^4 - 104x^3 + 16x^2 + 48x + 16	\( 2^{9}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.12.1356520905953125.1	x^12 - x^11 - 16x^10 + 20x^9 + 60x^8 - 69x^7 - 79x^6 + 88x^5 + 35x^4 - 45x^3 - x^2 + 7x - 1	\( 5^{6}\cdot 11^{4}\cdot 181^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.1521681143169024.2	x^12 - 4x^11 + 2x^10 + 12x^9 - 23x^8 - 8x^7 + 104x^6 - 192x^5 + 210x^4 - 160x^3 + 88x^2 - 32x + 8	\( 2^{33}\cdot 3^{11} \)	$S_3\wr C_2$ (as 12T35)	Trivial (GRH)
12.0.1711891286065152.5	x^12 + 6x^10 + 15x^8 + 24x^6 + 24x^4 + 24x^2 + 12	\( 2^{30}\cdot 3^{13} \)	$S_3\wr C_2$ (as 12T35)	$[2]$
12.0.1721085137518592.3	x^12 - 6x^11 + 29x^10 - 90x^9 + 242x^8 - 494x^7 + 893x^6 - 1262x^5 + 1594x^4 - 1514x^3 + 1309x^2 - 702x + 387	\( 2^{22}\cdot 17^{7} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.2742118830047232.1	x^12 - 12x^10 + 54x^8 - 108x^6 + 81x^4 - 12	\( -\,2^{18}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.2742118830047232.1	x^12 - 4x^9 + 54x^6 - 4x^3 + 1	\( 2^{18}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.5135673858195456.1	x^12 - 6x^10 - 4x^9 + 3x^8 + 36x^7 - 4x^6 - 48x^5 - 6x^4 + 16x^3 + 24x^2 - 8	\( -\,2^{30}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.5777633090469888.24	x^12 - 12x^10 - 8x^9 + 36x^8 + 60x^7 + 30x^6 - 3x^4 - 156x^3 - 54x^2 + 72x + 50	\( 2^{27}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.11277990709674579.1	x^12 - 12x^10 + 54x^8 - 97x^6 + 15x^4 + 99x^2 - 44	\( -\,3^{14}\cdot 11^{9} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.14280872991653888.1	x^12 - 2x^11 - 11x^10 + 14x^9 + 80x^8 - 218x^7 + 131x^6 + 218x^5 - 324x^4 + 82x^3 + 141x^2 - 46x - 17	\( -\,2^{22}\cdot 23^{7} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.15407021574586368.11	x^12 - 6x^10 + 27x^8 - 128x^6 + 336x^4 - 384x^2 + 192	\( 2^{30}\cdot 3^{15} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.15407021574586368.12	x^12 - 6x^10 - 12x^9 + 3x^8 + 108x^7 + 24x^6 - 216x^5 - 30x^4 - 176x^3 + 384x^2 + 192	\( 2^{30}\cdot 3^{15} \)	$S_3\wr C_2$ (as 12T35)	$[3]$
12.6.16515022032478208.1	x^12 - 5x^11 - x^10 + 26x^9 + 12x^8 - 48x^7 - 105x^6 - 39x^5 + 73x^4 + 66x^3 + 50x^2 + 48x + 16	\( -\,2^{13}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.37913186137014272.1	x^12 + 4x^10 + 2x^8 + 8x^6 + 25x^4 - 12x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$S_3\wr C_2$ (as 12T35)	$[6]$
12.6.41085390865563648.2	x^12 - 12x^10 - 8x^9 + 90x^8 + 24x^7 - 296x^6 - 72x^5 + 267x^4 - 48x^3 - 72x^2 + 72x - 18	\( -\,2^{33}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.41085390865563648.3	x^12 - 12x^10 - 16x^9 - 18x^8 - 72x^7 - 100x^6 - 48x^5 + 39x^4 + 112x^3 + 84x^2 + 24x - 2	\( -\,2^{33}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.41085390865563648.18	x^12 - 12x^10 + 18x^8 + 108x^6 + 153x^4 + 144x^2 + 72	\( 2^{33}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	$[2]$ (GRH)
12.0.41085390865563648.22	x^12 - 4x^11 + 10x^10 - 28x^9 + 91x^8 - 208x^7 + 460x^6 - 784x^5 + 1090x^4 - 1152x^3 + 888x^2 - 576x + 216	\( 2^{33}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T35)	$[2]$ (GRH)
12.6.46221064723759104.1	x^12 - 12x^10 + 18x^8 + 100x^6 - 351x^4 + 1224x^2 - 784	\( -\,2^{30}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T35)	Trivial (GRH)
12.6.51998697814228992.5	x^12 - 12x^10 - 4x^9 + 54x^8 + 36x^7 - 104x^6 - 108x^5 + 57x^4 + 132x^3 + 36x^2 - 72x - 12	\( -\,2^{27}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.51998697814228992.22	x^12 - 12x^10 - 12x^9 + 54x^8 + 108x^7 - 40x^6 - 324x^5 - 327x^4 + 204x^3 + 612x^2 + 360x + 52	\( -\,2^{27}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.175495605123022848.1	x^12 - 12x^10 + 54x^8 - 60x^6 - 207x^4 + 432x^2 - 192	\( -\,2^{24}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.339365979862212608.1	x^12 - 3x^11 - 14x^10 + 39x^9 + 87x^8 - 190x^7 - 197x^6 + 219x^5 - 342x^4 + 769x^3 + 2099x^2 - 318x + 18	\( 2^{13}\cdot 23^{10} \)	$S_3\wr C_2$ (as 12T35)	$[3]$
12.6.369768517790072832.1	x^12 - 12x^10 + 54x^8 - 44x^6 - 303x^4 + 576x^2 - 128	\( -\,2^{33}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.369768517790072832.84	x^12 - 12x^10 - 8x^9 + 54x^8 + 72x^7 + 96x^6 - 216x^5 - 1143x^4 + 1304x^3 + 1836x^2 - 3264x + 1388	\( 2^{33}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T35)	$[3]$
12.0.497393604742873088.1	x^12 - 6x^11 + 33x^10 - 110x^9 + 248x^8 - 398x^7 + 465x^6 - 398x^5 + 248x^4 - 110x^3 + 33x^2 - 6x + 1	\( 2^{22}\cdot 17^{9} \)	$S_3\wr C_2$ (as 12T35)	$[4]$
12.0.1247968747541495808.24	x^12 - 12x^10 + 90x^8 - 332x^6 + 873x^4 - 216x^2 + 48	\( 2^{30}\cdot 3^{19} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.0.1247968747541495808.36	x^12 - 8x^9 + 36x^8 + 96x^7 + 8x^6 - 432x^5 + 972x^4 + 288x^3 + 2160x^2 - 1152x + 528	\( 2^{30}\cdot 3^{19} \)	$S_3\wr C_2$ (as 12T35)	Trivial